ISEN 220 Introduction to Production and Manufacturing Systems Dr. Gary Gaukler

1. ISEN 220Introduction to Production and Manufacturing SystemsDr. Gary Gaukler

2. Quality and Profit • Profit = Revenue – Cost • Quality impacts on the revenue side: • Quality impacts on the cost side:

3. Defining Quality The totality of features and characteristics of a product or service that bears on its ability to satisfy stated or implied needs American Society for Quality

4. Costs of Quality • Prevention costs - reducing the potential for defects • Appraisal costs - evaluating products, parts, and services • Internal failure - producing defective parts or service before delivery • External costs - defects discovered after delivery

5. Costs of Quality • There is a tradeoff between the costs of improving quality, and the costs of poor quality • Philip Crosby (1979): • “Quality is free”

6. Inspection • Involves examining items to see if an item is good or defective • Detect a defective product • Does not correct deficiencies in process or product • It is expensive • Issues • When to inspect • Where in process to inspect

7. Inspection • Many problems • Worker fatigue • Measurement error • Process variability • Cannot inspect quality into a product • Robust design, empowered employees, and sound processes are better solutions

8. Statistical Process Control (SPC) • Uses statistics and control charts to tell when to take corrective action • Drives process improvement • Four key steps • Measure the process • When a change is indicated, find the assignable cause • Eliminate or incorporate the cause • Restart the revised process

9. Plots the percent of free throws missed 20% 10% 0% Upper control limit Coach’s target value | | | | | | | | | 1 2 3 4 5 6 7 8 9 Lower control limit Game number An SPC Chart Figure 6.7

10. Control Charts Constructed from historical data, the purpose of control charts is to help distinguish between natural variations and variations due to assignable causes

11. Statistical Process Control (SPC) • Variability is inherent in every process • Natural or common causes • Special or assignable causes • Provides a statistical signal when assignable causes are present • Detect and eliminate assignable causes of variation

12. Natural Variations • Also called common causes • Affect virtually all production processes • Expected amount of variation • Output measures follow a probability distribution • For any distribution there is a measure of central tendency and dispersion • If the distribution of outputs falls within acceptable limits, the process is said to be “in control”

13. Assignable Variations • Also called special causes of variation • Generally this is some change in the process • Variations that can be traced to a specific reason • The objective is to discover when assignable causes are present • Eliminate the bad causes • Incorporate the good causes

14. Each of these represents one sample of five boxes of cereal # # # # # Frequency # # # # # # # # # # # # # # # # # # # # # Weight Samples To measure the process, we take samples and analyze the sample statistics following these steps (a) Samples of the product, say five boxes of cereal taken off the filling machine line, vary from each other in weight Figure S6.1

15. The solid line represents the distribution Frequency Weight Samples To measure the process, we take samples and analyze the sample statistics following these steps (b) After enough samples are taken from a stable process, they form a pattern called a distribution Figure S6.1

16. Central tendency Variation Shape Frequency Weight Weight Weight Samples To measure the process, we take samples and analyze the sample statistics following these steps (c) There are many types of distributions, including the normal (bell-shaped) distribution, but distributions do differ in terms of central tendency (mean), standard deviation or variance, and shape Figure S6.1

17. Prediction Frequency Time Weight Samples To measure the process, we take samples and analyze the sample statistics following these steps (d) If only natural causes of variation are present, the output of a process forms a distribution that is stable over time and is predictable Figure S6.1

18. ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Prediction Frequency Time Weight Samples To measure the process, we take samples and analyze the sample statistics following these steps (e) If assignable causes are present, the process output is not stable over time and is not predicable Figure S6.1

19. The mean of the sampling distribution (x) will be the same as the population mean m x = m s n The standard deviation of the sampling distribution (sx) will equal the population standard deviation (s) divided by the square root of the sample size, n sx = Central Limit Theorem Regardless of the distribution of the population, the distribution of sample means drawn from the population will tend to follow a normal curve

20. Three population distributions Mean of sample means = x Beta Standard deviation of the sample means Normal = sx = Uniform s n | | | | | | | -3sx -2sx -1sx x +1sx +2sx +3sx 95.45% fall within ± 2sx 99.73% of all x fall within ± 3sx Population and Sampling Distributions Distribution of sample means Figure S6.3

21. For variables that have continuous dimensions • Weight, speed, length, strength, etc. • x-charts are to control the central tendency of the process • R-charts are to control the dispersion of the process • These two charts must be used together Control Charts for Variables

22. For x-Charts when we know s Upper control limit (UCL) = x + zsx Lower control limit (LCL) = x - zsx where x = mean of the sample means or a target value set for the process z = number of normal standard deviations sx = standard deviation of the sample means = s/ n s = population standard deviation n = sample size Setting Chart Limits

23. Hour 1 Box Weight of Number Oat Flakes 1 17 2 13 3 16 4 18 5 17 6 16 7 15 8 17 9 16 Mean 16.1 s = 1 Hour Mean Hour Mean 1 16.1 7 15.2 2 16.8 8 16.4 3 15.5 9 16.3 4 16.5 10 14.8 5 16.5 11 14.2 6 16.4 12 17.3 n = 9 UCLx = x + zsx= 16 + 3(1/3) = 17 ozs LCLx = x - zsx = 16 - 3(1/3) = 15 ozs Setting Control Limits For 99.73% control limits, z = 3

24. Variation due to assignable causes Out of control 17 = UCL Variation due to natural causes 16 = Mean 15 = LCL Variation due to assignable causes | | | | | | | | | | | | 1 2 3 4 5 6 7 8 9 10 11 12 Out of control Sample number Setting Control Limits Control Chart for sample of 9 boxes

25. For x-Charts when we don’t know s Upper control limit (UCL) = x + A2R Lower control limit (LCL) = x - A2R where R = average range of the samples A2 = control chart factor found in Table S6.1 x = mean of the sample means Setting Chart Limits

26. Sample Size Mean Factor Upper Range Lower Range n A2D4D3 2 1.880 3.268 0 3 1.023 2.574 0 4 .729 2.282 0 5 .577 2.115 0 6 .483 2.004 0 7 .419 1.924 0.076 8 .373 1.864 0.136 9 .337 1.816 0.184 10 .308 1.777 0.223 12 .266 1.716 0.284 Control Chart Factors Table S6.1

27. Process average x = 16.01 ounces Average range R = .25 Sample size n = 5 Setting Control Limits

28. Process average x = 16.01 ounces Average range R = .25 Sample size n = 5 UCLx = x + A2R = 16.01 + (.577)(.25) = 16.01 + .144 = 16.154 ounces UCL = 16.154 Mean = 16.01 LCLx = x - A2R = 16.01 - .144 = 15.866 ounces LCL = 15.866 Setting Control Limits